Scientific notation root powers exponents question

AI Thread Summary
The discussion centers on calculating the fourth root of the square root of 5.2 x 10^-9 in scientific notation. The user arrives at an answer of ±8.5 x 10^-3, while the textbook provides ±2.7 x 10^-2. Confusion arises regarding the manipulation of exponents and the interpretation of the roots involved. Clarification is sought on whether the expression should be treated as the eighth root of the entire term or just the numerical part. The conversation emphasizes the importance of correctly applying exponent rules in scientific notation calculations.
DkEnrgyFrk
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Homework Statement



scientific notation

I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power

Homework Equations



4 . .... ... ... -9
... sq rt of 5.2 X 10

Code:
4                        -9
   sq rt of 5.2 X 10

The Attempt at a Solution



The answer I get is +- 8.5 x 10 to the negative 3rd power
but the book is giving me an answer of +- 2.7 x 10 to the -2nd power

I get the +- because it's an even root which means an absolute or + or - number can be squared.
I moved the decimal place 3 places to the right so that the power of -12 can be easily divided by the power of 4.
I tried reversing the decimal place as well so that the power is -8.
I am not getting why I am not coming up with the same answer as the book. I really believe the book is in error.
Can anyone verify either of these and please explain what I am doing wrong if I am incorrect?

Thank you so much in advance.
 
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DkEnrgyFrk said:

Homework Statement



scientific notation

I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power

Homework Equations



4 . .... ... ... -9
... sq rt of 5.2 X 10

Code:
4                        -9
   sq rt of 5.2 X 10

The Attempt at a Solution



The answer I get is +- 8.5 x 10 to the negative 3rd power
but the book is giving me an answer of +- 2.7 x 10 to the -2nd power

I get the +- because it's an even root which means an absolute or + or - number can be squared.
I moved the decimal place 3 places to the right so that the power of -12 can be easily divided by the power of 4.
I tried reversing the decimal place as well so that the power is -8.
I am not getting why I am not coming up with the same answer as the book. I really believe the book is in error.
Can anyone verify either of these and please explain what I am doing wrong if I am incorrect?

Thank you so much in advance.

Your descriptions are ambiguous. Is this what you mean?
\sqrt[4]{\sqrt{5.2~ X~ 10^{-9}}}

Or is it this?
\sqrt[4]{\sqrt{5.2}}~X~10^{-9}

In either case, the fourth root of the square root is the eighth root.
 
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